Question

A body of mass $m$ is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released, it oscillates with a time period of $3s$. When the mass $m$ is increased by $1kg$, the time period of oscillation becomes $5s$. The value of $m$ in $kg$ is

• A. $\frac{9}{16}$
• B. $\frac{3}{4}$
• C. $\frac{4}{3}$
• D. $\frac{16}{9}$

Answer 1

The correct option is A $\frac{9}{16}$

The time period of a spring mass system
$T=2\pi \sqrt{\frac{m}{k}}$

Initially,
$3=2\pi \sqrt{\frac{m}{k}}$

After increasing the mass,
$5=2\pi \sqrt{\frac{m+1}{k}}$

Dividing the equations,
$\frac{3}{5}=\sqrt{\frac{m}{m+1}}$
$\frac{9}{25}=\frac{m}{m+1}$

Solving, we get $m=\frac{9}{16}kg$